Compactification of the heterotic pure spinor superstring i

In this paper we begin the study of compactifications of the pure spinor formalism for superstrings. As a first example of such a process we study the case of the heterotic string in a Calabi-Yau background. We explicitly construct a BRST operator imposing N = 1 four-dimensional supersymmetry and show that nilpotence implies Kähler and Ricci-flatness conditions. The massless spectrum is computed using this BRST operator and it agrees with the expected result.